Similar polygons
State if polygons are similar

Answer:

The area of the irregular figure is 8.1 ft² (rounded to the nearest tenth).

Step-by-step explanation:

The irregular figure is made up of:

[tex]\boxed{\begin{aligned}\sf Area\;of\;triangle&=\sf \dfrac{1}{2} \times base \times height\\\\&=\sf \dfrac{1}{2} \times 2.8 \times 3.6\\\\&=\sf 1.4 \times 3.6\\\\&=\sf 5.04 \; ft^2\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\sf Area \; of\;semicircle&= \sf \dfrac{1}{2} \pi r^2\\\\&= \sf \dfrac{1}{2}\times 3.14 \times (1.4)^2\\\\&= \sf \dfrac{1}{2}\times 3.14 \times1.96\\\\&= \sf 1.57 \times1.96\\\\&= \sf 3.0772\; ft^2\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\sf Area \;of\;irregular\;figure&=\sf Area\;of\;triangle+ Area\;of\;semicircle\\\\&=\sf 5.04+3.0772\\\\&=\sf 8.1172\\\\&=\sf 8.1\; ft^2\;(nearest\;tenth)\end{aligned}}[/tex]

Therefore, the area of the irregular figure is 8.1 ft² rounded to the nearest tenth.

Answer:

27.52

Step-by-step explanation:

1m =1.09 yards

30/1.09 = 27.52

Answer:

Step-by-step explanation:

tan L = 8/15

Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)

Answer:

As P(M) = 0.45

P(F) = 1-0.45 = 0.55

P(Both students are male) = 0.45 x 0.45 = 0.2025 = 0.203 (cor to 3 dp)

P(Both students are female) = (1-0.45) x (1-0.45) = 0.55 x 0.55 = 0.3025 = 0.303 (cor to 3 dp)

P(First student male and second female) = 0.45 x 0.55 = 0.2475 = 0.248 (cor to 3 dp)

hope this helps!!!

The height of the right cylinder is 0.011 inches approximately.

Volume Definition:

Every three-dimensional object occupies some space. It is being determined how big this area is. Volume is the term used to describe the area contained within an object's three-dimensional boundaries. It is referred to as the object's capability on sometimes.

‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Now in the given question,

Circumference,

[tex]2\pi r[/tex] = [tex]\frac{41}{4}[/tex]

[tex]r=\frac{41}{8\pi }[/tex]

V = 9 cubic inches

volume of cylinder = πr²h = 3.14×[tex]\frac{41}{8\pi }^2[/tex]×h

h = (9)÷(3.14×[tex]\frac{41}{8\pi }^2[/tex]) = 0.011 inches

therefore the height of the cylinder is 0.011 inches approximately.

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The expression with exactly two terms for the amount of money the club

will make for selling 'f' frames is 7f- 36.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Given:

Price of frame= $13

Material cost = $6

Renting both cost = $36

For selling 'f' frames the amount of money the club make

= (13f - 6f) - 36

= (13-6)f- 36

= 7f- 36

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The coordinates can be determined by using mid point formula. Here the coordinates vertex C is (2,8), vertex A is (0,2) and vertex T is (6,4)

Here the midpoints are (1,5) , (4,6), (3,3).

By using mid point equation, x₁+x₂/2 = 1

So x₁+x₂ = 2  --------------------> eq 1

x₂+x₃/2 = 3

x₂+x₃ = 6   -----------------------> eq 2

x₁+x₃/2 = 4

x₁+x₃ = 8 -----------------------> eq 3

Adding equations 1,2,3

2( x₁+x₂+x₃) = 16

 x₁+x₂+x₃ = 8 ---------------> 4

Determining x-coordinates

Subtracting equation 1 from 4

x₁+x₂+x₃ -(x₁+x₂) = 8-2

 x₃ = 6

Similarly subtracting equation 2 from 4

x₁+x₂+x₃ -(x₂-x₃) = 8-6

x₁ = 2

Subtracting 3 from 4

x₁+x₂+x₃ -(x₁+x₃) = 8-8

x₂ = 0

Determining y coordinates

y₁+y₂/2 = 5

y₁+y₂ = 10 ----------------> 5

y₁+y₃/2 = 6

y₁+y₃ = 12 ----------------> 6

y₂+y₃/2 = 3

y₂+y₃ =6   -------------->  7

Adding equations 5,6 and 7

2(y₁+y₂+y₃) = 28

y₁+y₂+y₃ = 14 -----------------> 8

Subtracting equations 5,6 and 7 from 8

y₁+y₂+y₃ -(y₁+y₂) =14 - 10

y₃ = 4

y₁+y₂+y₃ -( y₂+y₃) = 14- 6

y₁ = 8

y₁+y₂+y₃-(y₁+y₃) = 14- 12 = 2

So the coordinates are (x₁ , y₁) =(2,8)

                                       (x₂, y₂) = (0, 2)

                                       (x₃, y₃) = (6,4)

So the coordinates of C,A and T are (2,8) , (0,2) and (6,4) respectively.

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Answer:

21°

Step-by-step explanation:

For this right-angled triangle:

∠M = angle in question

Side LM = Hypotenuse

With respect to ∠M:

Side LN = Opposite side

Side MN = Adjacent side

Trigonometric function applied:

sin∠M = [tex]\frac{opposite}{hypotenuse}[/tex]

           = [tex]\frac{8}{22}[/tex]

 ∠M = [tex]sin^{-1} (\frac{8}{22})[/tex]

          = 21.32°

  ∠M  = 21° (Rounded to the nearest degree)

Answer:

∠M = 21°

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Therefore, substitute the given values into the sine ratio and solve for ∠M:

[tex]\implies \sin(M)=\dfrac{8}{22}[/tex]

[tex]\implies M=\arcsin \left(\dfrac{8}{22}\right)[/tex]

[tex]\implies M=21.323686...^{\circ}[/tex]

[tex]\implies M=21^{\circ}\sf\;(nearest\;degree)[/tex]

Therefore, the measure of ∠M to the nearest degree is 21°.

Answer:

An inequality in mathematics is a statement that compares two values, with the use of inequality symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≠ (not equal to). For example, the inequality "5 > 2" states that 5 is greater than 2. Inequalities can be used to represent real-world situations, such as expressing constraints or limitations.

Step-by-step explanation:

Answer:

k = 176

Step-by-step explanation:

16 = k/11

16 * 11 = k/11 * 11

176 = k

Because k is being divided by 11 on the right-hand side of the equation, we would need to multiply both sides by 11 to undo the division operation done to k so we can isolate it.

The cost of one candy bar is $2.35.

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service.

Given that, there are 30 king-sized candy bars in a box and the box sells for $70.50, we need to find that how much does each candy bar in the box cost,

Since, the cost of all 30 candies is given collectively, i.e. $70.50,

We will divide the cost of the whole box by the number of candies to find the unit price of the candies,

Unit price = $70.50 / 30

= $2.35

Hence, the cost of one candy bar is $2.35.

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Step-by-step explanation:

In order to make a profit R > C

So let's make those equal first

R = C

[tex]6.56x = 10.063 + 1.09x[/tex]

Let's get X alone by subtracting 1.09x from both sides.

[tex]5.47x = 10.063[/tex]

Next we divide by 5.47

[tex]x = 1.83[/tex]

Rounding up to 2, looks like Anna needs to only sell 2 books to start making a profit

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 5: 3, (girls: boys) we can use this equation to figure out how many boys there are if there are 35 girls:

We can see that in the ratio 5: 3, 5 is being multiplied by 0.6 to get three. If the relationship between the numbers 5 and 35 stays proportional, we multiply 35 by 0.6.

Therefore, the ratio of girls to boys is 35: 21, meaning there are 21 boys.

Answer:

h = F/4g

Step-by-step explanation:

Answer:

3/4 servings

Step-by-step explanation:

Each serving = 1/2

There are 3/8 cookies.

How many times 1/2 "fits" into 3/8 = how many servings.

3/8 / 1/2

= 3/8 * 2

= 3/4 servings

Answer:

12

Step-by-step explanation:

6 - 3/4x + 1/3 = 1/2x + 5

6 - 9/12x + 4/12 = 6/12x + 5  If I multiply all the way through by 12 I will eliminate the fraction

72 - 9x + 4 = 6x+ 60

The multiplication equation best represents the figure will be 6 x 0.32 = 1.92. Then the correct option is B.

Algebra is the examination of ideational signs while reasoning the manipulation of all those thoughts.

The big square block represents the 1 unit. And each small block represents 0.01 units.

The number of small blocks which are marked by the color in one shot is 32 which means 0.32 units.

And these processes are done six times, then the expression that represents the condition is given as,

6 x 0.32 = 1.92

The multiplication equation best represents the figure will be 6 x 0.32 = 1.92. Then the correct option is B.

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Answer:

give me more instructions so i can actually help

Step-by-step explanation:

Given the set of data used, This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

An observational study draws conclusions from a sample of a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or practical limitations.

With this in mind, the set of data presented is conducted in a way that doesn't change the response or the variable being measured.

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Answer:

where represents the time two hours later than the current time. represents the time one hour later than current time. Henceforth, the time at present is 9 pm.

Step-by-step explanation:

Bistro’s food cost percent is 35.83%

Food cost percentage is calculated by taking the cost of goods sold and dividing that by the revenue or sales generated from that finished dish.

Food cost percent is calculated using the following formula:

Total Food Cost Percentage = (Total Cost of Goods Sold / Total Revenue) x 100

From the parameters in the question,

Total Food Cost Percentage = 67,000/187,000 x 100

Total Food Cost Percentage = 6,700,000/187000

Total Food Cost Percentage = 35.73%

Hence, the Bistro’s food cost percent is 35.83%

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Answer:

see below

Step-by-step explanation:

170*70=11900

after one year 170*80 = 13600
gain on paper = 13600-11900 = 1700

80/70 = 1.14 so 14% if you had paid out of pocket

but then you bought on margin meaning you only used

15% of your money = 11900* 15% = 1785

but your gain was 1700, so your return = 1700/1785 = 95%

45% of your money = 11900* 45% = 5355

but your gain was 1700, so your return = 1700/5355 = 32%

85% of your money = 11900* 85% = 10115

but your gain was 1700, so your return = 1700/10115 = 17%

Answer: Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk.

We know that:

x + y = 7 (because you want 7 days of supply)

And the protein content per serving of Designer Whey is 18g and the protein content per serving of Muscle Milk is 20g. So:

18x + 20y = 412 (because you want 412g of protein)

And the carbohydrate content per serving of Designer Whey is 4g and the carbohydrate content per serving of Muscle Milk is 8g. So:

4x + 8y = 108 (because you want 108g of carbohydrates)

We can now use the above two equations to solve for x and y. We'll start by solving for x in terms of y:

18x + 20y = 412

18x = 412 - 20y

x = (412 - 20y)/18

Now we can substitute this expression for x into the equation for the carbohydrates:

4x + 8y = 108

4((412 - 20y)/18) + 8y = 108

1664 - 80y + 8y = 1080

1664 = 1080 + 80y

584 = 80y

y = 7.3

Since y must be an integer, we'll round it down to 7. So y = 7. We can now use either equation to find x:

18x + 20y = 412

18x + 20 * 7 = 412

18x = 412 - 140

18x = 272

x = 15.1

Since x must be an integer, we'll round it up to 15. So x = 15.

Therefore, you should combine 15 servings of Designer Whey and 7 servings of Muscle Milk in order to meet your requirements.

Step-by-step explanation:

Answer:

  D. y = x² +7x +10

Step-by-step explanation:

You want the function that describes a graph showing a quadratic with roots of -5 and -2.

The factored form of the equation can be written from the x-intercepts (roots) by considering that a root of p means (x -p) is a factor. The factored equation is ...

  y = (x -(-5))(x -(-2)) = (x +5)(x +2) . . . . . doesn't match A or B

When this is multiplied out, it becomes ...

  y = x² +5x +2x +10 = x² +7x +10 . . . . . . matches choice D

The equation is y = x² +7x +10.

Answer:

y = -140x + 1400

Step-by-step explanation:

First, we'll find the slope, m, using the formula:

m = (160 - 780) / (8 - 4) = -620 / 4 = -155

Next, we'll use one of the points and the slope to find the y-intercept, b:

b = y - mx

We'll use the point (4, 780) to find b:

b = 780 - (4 * -155) = 1400

So the equation that models the balance, y, after x months is:

y = -155x + 1400

And since -155 can be simplified to -140, the equation becomes:

y = -140x + 1400

a) The total time taken in hours is 0.75 hours

b) The amount of all-purpose flour needed is not given in the question.

c) The thickness of the dough in centimetres is not given.

d) The amount of salt needed per scone is not given.

e) The amount of butter needed per scone is not given.

f) It will be ready for consumption by 15:30

g) 356°F in °C can be calculated using the formula:

°C = (356°F - 32°) / 1.8 = 180°C.

a) Total preparation and cooking time = 30 minutes + 15 minutes = 45 minutes = 0.75 hours

b) To bake 36 scones, we need:

36 scones * all-purpose flour needed to bake 1 scone = all-purpose flour needed to bake 36 scones

The amount of all-purpose flour needed is not given.

c) The thickness of the dough in centimetres is not given.

d) Mrs. Msimango baked 48 scones, so the number of teaspoons of salt required would be:

48 scones * teaspoons of salt needed per scone = teaspoons of salt needed for 48 scones

The amount of salt needed per scone is not given.

e) Mrs. Msimango baked 48 scones, so the number of millilitres of butter required would be:

48 scones * ml of butter needed per scone = ml of butter needed for 48 scones

The amount of butter needed per scone is not given.

f) If Mrs. Msimango started making the scones at 14:55, they would be ready to eat at 14:55 + 0.75 hours = 15:30.

g) 356°F in °C can be calculated using the formula:

°C = (356°F - 32°) / 1.8 = 180°C

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